If x⁴ + x²y²+ y⁴ = 21/256 and x² + xy + y² = 3/16, then…

If x⁴ + x²y²+ y⁴ = 21/256 and x² + xy + y² = 3/16, then 2(x² + y²) = ?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 5/8

Application

x⁴ + x²y²+ y⁴ = 21/256 ............(1)

By adding and subtracting x²y² in (1)

we get, x⁴ + 2x²y²+ y⁴ - x²y²

(x² + y² + xy)(x² + y² - xy) = 21/256

By using the formula (a² - b²) = (a + b) (a - b)

3/16(x² + xy - y²) = 7/16

(x² + xy - y²) = 7/16........ (a)

(x² + xy + y² ) = 3/16.........(b)

adding a and b

2(x² + y²) = 10/16 = 5/8

SSC CPO 2019 PYQ — Question 112